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arXiv · 1611.09730

Prime spectra of ambiskew polynomial rings

Christopher D. Fish·David A. Jordan
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Abstract

We determine criteria for the prime spectrum of an ambiskew polynomial algebra $R$ over an algebraically closed field $K$ to be akin to those of two of the principal examples of such an algebra, namely the universal enveloping algebra $U(sl_2)$ (in characteristic $0$) and its quantization $U_q(sl_2)$ (when $q$ is not a root of unity). More precisely, we aim to determine when the prime spectrum of $R$ consists of $0$, the ideals $(z-λ)R$ for some central element $z$ of $R$ and all $λ\in K$, and, for some positive integer $d$ and each positive integer $m$, $d$ height two prime ideals with Goldie rank $m$. New applications are to certain ambiskew polynomial rings over coordinate rings of quantum tori which arise, as localizations of connected quantized Weyl algebras.

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Christopher D. Fish, David A. Jordan. 2018-01-30. Prime spectra of ambiskew polynomial rings. https://doi.org/10.1017/s0017089518000046

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